A positive definite estimator of the non stationary covariance of random fields

Gilles Guillot; R. Senoussi; P. Monestiez

doi:10.1007/978-94-010-0810-5_29

A positive definite estimator of the non stationary covariance of random fields

Gilles Guillot, R. Senoussi, P. Monestiez

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Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Abstract

This paper proposes a non parametric estimator of the covariance function for 2-dimensional random fields by regularization of the empirical covariance matrix by a convolution kernel. The main feature of this estimator is its positive definiteness everywhere on its domain while it does not assume stationarity of the field. We present several choices of the kernel, then we provide some insight for the selection of the smoothing parameter involved. We illustrate some of our results on a one dimensional simulated dataset and on actual 2-dimensional rainfall data.

Original language	English
Title of host publication	geoENV III — Geostatistics for Environmental Applications : Proceedings of the Third European Conference on Geostatistics for Environmental Applications held in Avignon, France, November 22–24, 2000
Editors	Pascal Monestiez, Denis Allard, Roland Froidevaux
Publication date	2001
Pages	333-344
ISBN (Print)	978-0-7923-7107-6
ISBN (Electronic)	978-94-010-0810-5
DOIs	https://doi.org/10.1007/978-94-010-0810-5_29
Publication status	Published - 2001
Externally published	Yes
Event	3rd European Conference on Geostatistics for Environmental Applications - Avignon, France Duration: 22 Nov 2000 → 24 Nov 2000 Conference number: 3 https://link.springer.com/book/10.1007/978-94-010-0810-5

Conference

Conference	3rd European Conference on Geostatistics for Environmental Applications
Number	3
Country/Territory	France
City	Avignon
Period	22/11/2000 → 24/11/2000
Internet address	https://link.springer.com/book/10.1007/978-94-010-0810-5

Series	Quantitative Geology and Geostatistics
Volume	11
ISSN	0924-1973

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Guillot, G., Senoussi, R., & Monestiez, P. (2001). A positive definite estimator of the non stationary covariance of random fields. In P. Monestiez, D. Allard, & R. Froidevaux (Eds.), geoENV III — Geostatistics for Environmental Applications: Proceedings of the Third European Conference on Geostatistics for Environmental Applications held in Avignon, France, November 22–24, 2000 (pp. 333-344) https://doi.org/10.1007/978-94-010-0810-5_29

Guillot, Gilles ; Senoussi, R. ; Monestiez, P. / A positive definite estimator of the non stationary covariance of random fields. geoENV III — Geostatistics for Environmental Applications: Proceedings of the Third European Conference on Geostatistics for Environmental Applications held in Avignon, France, November 22–24, 2000. editor / Pascal Monestiez ; Denis Allard ; Roland Froidevaux. 2001. pp. 333-344 (Quantitative Geology and Geostatistics, Vol. 11).

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abstract = "This paper proposes a non parametric estimator of the covariance function for 2-dimensional random fields by regularization of the empirical covariance matrix by a convolution kernel. The main feature of this estimator is its positive definiteness everywhere on its domain while it does not assume stationarity of the field. We present several choices of the kernel, then we provide some insight for the selection of the smoothing parameter involved. We illustrate some of our results on a one dimensional simulated dataset and on actual 2-dimensional rainfall data. ",

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Guillot, G, Senoussi, R & Monestiez, P 2001, A positive definite estimator of the non stationary covariance of random fields. in P Monestiez, D Allard & R Froidevaux (eds), geoENV III — Geostatistics for Environmental Applications: Proceedings of the Third European Conference on Geostatistics for Environmental Applications held in Avignon, France, November 22–24, 2000. Quantitative Geology and Geostatistics, vol. 11, pp. 333-344, 3rd European Conference on Geostatistics for Environmental Applications, Avignon, France, 22/11/2000. https://doi.org/10.1007/978-94-010-0810-5_29

A positive definite estimator of the non stationary covariance of random fields. / Guillot, Gilles; Senoussi, R.; Monestiez, P.
geoENV III — Geostatistics for Environmental Applications: Proceedings of the Third European Conference on Geostatistics for Environmental Applications held in Avignon, France, November 22–24, 2000. ed. / Pascal Monestiez; Denis Allard; Roland Froidevaux. 2001. p. 333-344 (Quantitative Geology and Geostatistics, Vol. 11).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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Guillot G, Senoussi R, Monestiez P. A positive definite estimator of the non stationary covariance of random fields. In Monestiez P, Allard D, Froidevaux R, editors, geoENV III — Geostatistics for Environmental Applications: Proceedings of the Third European Conference on Geostatistics for Environmental Applications held in Avignon, France, November 22–24, 2000. 2001. p. 333-344. (Quantitative Geology and Geostatistics, Vol. 11). doi: 10.1007/978-94-010-0810-5_29

A positive definite estimator of the non stationary covariance of random fields

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